Question: Solve for $x$ and $y$ using elimination. ${3x+5y = 75}$ ${-3x-6y = -84}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $3x$ and $-3x$ cancel out. $-y = -9$ $\dfrac{-y}{{-1}} = \dfrac{-9}{{-1}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {3x+5y = 75}\thinspace$ to find $x$ ${3x + 5}{(9)}{= 75}$ $3x+45 = 75$ $3x+45{-45} = 75{-45}$ $3x = 30$ $\dfrac{3x}{{3}} = \dfrac{30}{{3}}$ ${x = 10}$ You can also plug ${y = 9}$ into $\thinspace {-3x-6y = -84}\thinspace$ and get the same answer for $x$ : ${-3x - 6}{(9)}{= -84}$ ${x = 10}$